Zero mean curvature surfaces in isotropic space with planar curvature lines

2024/10/24 by Joseph Cho, Cho, Joseph, Masaya Hara +1
Mathematics · #53A10 (Primary) 53A15 #53A35 #53B30 (Secondary) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Mathematics and Applications

paper · pdf · doi:10.48550/arxiv.2410.18728

openalex publication_date 2024/10/24 · openalex created_date 2024/11/13 · openalex updated_date 2026/07/28

Abstract

We give a comprehensive account of zero mean curvature surfaces in isotropic 3-space with planar curvature lines. After giving a complete classification all such surfaces, we show that they belong to a 1-parameter family of surfaces. We then investigate their relationship to Thomsen-type surfaces in isotropic 3-space, those zero mean curvature surfaces in isotropic 3-space that are also affine minimal.

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